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Global Results on Exponential Stability of Neutral Cohen–Grossberg Neural Networks Involving Multiple Neutral and Discrete Time-Varying Delays: A Method Based on System Solutions

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Abstract

In this paper, we study the global exponential stability of a class of neutral-type Cohen–Grossberg neural networks (NTCGNNs) with multiple discrete and neutral time varying delays. Since the network model cannot be represented in the form of vector–matrix, a method based on system solutions is proposed to establish novel global exponential stability criteria for the NTCGNNs under consideration. This method can results in global exponential stability criteria consists of only a few linear scalar inequalities, and it does not need to set up any Lyapunov–Krasovskii functionals, which can greatly reduce a large amount of computations. Compared with the existing ones, the applicability of the obtained stability conditions are explained by two representative numerical examples. It is worth emphasizing that the method ground upon system solutions is first proposed, and is applicable for system models which can or cannot be represented in the form of vector–matrix.

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References

  1. Dong Z, Wang X, Zhang X, Hu M, Dinh TN (2023) Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption. Nonlinear Anal Hybrid Syst 47:101291

    MathSciNet  MATH  Google Scholar 

  2. Chen Y, Zhang X, Xue Y (2022) Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays. Math Comput Simul 193:173–189

    MathSciNet  MATH  Google Scholar 

  3. Abdelaziz M, Chérif F (2020) Exponential lag synchronization and global dissipativity for delayed fuzzy Cohen-Grossberg neural networks with discontinuous activations. Neural Process Lett 51(2):1653–1676

    Google Scholar 

  4. Townsend J, Chaton T, Monteiro JM (2020) Extracting relational explanations from deep neural networks: a survey from a neural-symbolic perspective. IEEE Trans Neural Netw Learn Syst 31(9):3456–3470

    MathSciNet  Google Scholar 

  5. Zhou L, Zhao Z (2020) Asymptotic stability and polynomial stability of impulsive Cohen-Grossberg neural networks with multi-proportional delays. Neural Process Lett 51(3):2607–2627

    Google Scholar 

  6. Cao J, Liang J (2004) Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J Math Anal Appl 296(2):665–685

    MathSciNet  MATH  Google Scholar 

  7. Faydasicok O (2020) An improved Lyapunov functional with application to stability of Cohen-Grossberg neural networks of neutral-type with multiple delays. Neural Netw 132:532–539

    MATH  Google Scholar 

  8. Shi KB, Zhong SM, Zhu H, Liu XZ, Zeng Y (2015) New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays. Neurocomputing 168:896–907

    Google Scholar 

  9. Shi KB, Zhu H, Zhong SM, Zeng Y, Zhang YP (2015) New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach. J Franklin Inst 352(1):155–176

    MathSciNet  MATH  Google Scholar 

  10. Hu W, Qiao X, Dong T (2021) Spatiotemporal dynamic of a coupled neutral-type neural network with time delay and diffusion. Neural Comput Appl 33(12):6415–6426

    Google Scholar 

  11. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern Syst 13(5):815–826

    MathSciNet  MATH  Google Scholar 

  12. Zheng P, Zhang J, Tang W (2010) Color image associative memory on a class of Cohen-Grossberg networks. Pattern Recogn 43(10):3255–3260

    MATH  Google Scholar 

  13. Wang X, Park JH, Liu H, Zhang X (2021) Cooperative output-feedback secure control of distributed linear cyber-physical systems resist intermittent DoS attacks. IEEE Trans Cybern 51(10):4924–4933

    Google Scholar 

  14. Wang X, Yang GH (2020) Fault-tolerant consensus tracking control for linear multiagent systems under switching directed network. IEEE Trans Cybern 50(5):1921–1930

    Google Scholar 

  15. Wang X, Cao J, Yang B, Chen F (2022) Fast fixed-time synchronization control analysis for a class of coupled delayed Cohen-Grossberg neural networks. J Franklin Inst 359(4):1612–1639

    MathSciNet  MATH  Google Scholar 

  16. Li H, Zhao N, Wang X, Zhang X, Shi P (2019) Necessary and sufficient conditions of exponential stability for delayed linear discrete-time systems. IEEE Trans Autom Control 64(2):712–719

    MathSciNet  MATH  Google Scholar 

  17. Long F, Zhang CK, He Y, Wang QG, Wu M (2022) Stability analysis for delayed neural networks via a novel negative-definiteness determination method. IEEE Trans Cybern 52(6):5356–5366

    Google Scholar 

  18. Wan L, Zhou Q (2021) Exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying delays. IEEE Access 9:48914–48922

    Google Scholar 

  19. Zhang X, Wang Y, Wang X (2021) A direct parameterized approach to global exponential stability of neutral-type Cohen-Grossberg neural networks with multiple discrete and neutral delays. Neurocomputing 463:334–340

    Google Scholar 

  20. Faydasicok O (2021) Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays. Discrete Contin Dyn Syst-S 14(4):1245–1258

    MathSciNet  MATH  Google Scholar 

  21. Faydasicok O (2020) A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays. Neural Netw 129:288–297

    MATH  Google Scholar 

  22. Faydasicok O (2020) New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays. Neural Netw 125:330–337

    MATH  Google Scholar 

  23. Faydasicok O (2020) New results on stability of delayed Cohen-Grossberg neural networks of neutral type. Complexity 2020:1973548

    MATH  Google Scholar 

  24. Arik S (2019) A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays. J Franklin Inst 356:276–291

    MathSciNet  MATH  Google Scholar 

  25. Arik S (2020) New criteria for stability of neutral-type neural networks with multiple time delays. IEEE Trans Neural Netw Learn Syst 31(5):1504–1513

    MathSciNet  Google Scholar 

  26. Wan L, Zhou Q, Fu H, Zhang Q (2021) Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. AIMS Math 6(8):8030–8043

    MathSciNet  MATH  Google Scholar 

  27. Gholami Y (2021) Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional. Adv Differ Equ 2021(1):112

    MathSciNet  MATH  Google Scholar 

  28. Wan L, Zhou Q (2020) Stability analysis of neutral-type Cohen-Grossberg neural networks with multiple time-varying delays. IEEE Access 8:27618–27623

    Google Scholar 

  29. Faydasicok O, Arik S (2022) A novel Lyapunov stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays. Neural Netw 155:330–339

    MATH  Google Scholar 

  30. Zhang G, Wang T, Li T, Fei S (2018) Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks. Neurocomputing 275:1782–1792

    Google Scholar 

  31. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci 81:3088–3092

    MATH  Google Scholar 

  32. Bélair J (1993) Stability in a model of a delayed neural network. J Dyn Diff Equ 5(4):607–623

    MathSciNet  MATH  Google Scholar 

  33. Lu K, Xu D, Yang Z (2006) Global attraction and stability for Cohen-Grossberg neural networks with delays. Neural Netw 19:1538–1549

    MATH  Google Scholar 

  34. Mandal S, Majee NC (2011) Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays. Neurocomputing 74:1000–1007

    Google Scholar 

  35. Plemmons RJ (1977) M-matrix characterizations. I-nonsingular M-matrices. Linear Algebra Appl 18(2):175–188

    MathSciNet  MATH  Google Scholar 

  36. Ozcan N (2019) Stability analysis of Cohen-Grossberg neural networks of neutral-type: multiple delays case. Neural Netw 113:20–27

    MATH  Google Scholar 

  37. Senan S, Yucel E, Orman Z, Samli R, Arik S (2021) A novel Lyapunov functional with application to stability analysis of neutral systems with nonlinear disturbances. Discrete Contin Dyn Syst-S 14(4):1415–1428

    MathSciNet  MATH  Google Scholar 

  38. Kwon OM, Lee SH, Park MJ (2022) Some novel results on stability analysis of generalized neural networks with time-varying delays via augmented approach. IEEE Trans Cybern 52(4):2238–2248

    Google Scholar 

  39. Chen J, Zhang XM, Park JH, Xu S (2022) Improved stability criteria for delayed neural networks using a quadratic function negative-definiteness approach. IEEE Trans Neural Netw Learn Syst 33(3):1348–1354

    MathSciNet  Google Scholar 

  40. Hu X, Liu X, Tang M (2022) Stability analysis of delayed neural network based on the convex method and the non-convex method. Neurocomputing 483:275–285

    Google Scholar 

  41. Chen J, Park JH, Xu S (2022) Stability analysis for delayed neural networks with an improved general free-matrix-based integral inequality. IEEE Tran Neural Netw Learn Syst 31(2):675–684

    MathSciNet  Google Scholar 

  42. Huang C, Su R, Cao J, Xiao S (2020) Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators. Math Comput Simul 171:127–135

    MathSciNet  MATH  Google Scholar 

  43. Qian C (2021) New periodic stability for a class of Nicholson’s blowflies models with multiple different delays. Int J Control 94(12):3433–3438

    MathSciNet  MATH  Google Scholar 

  44. Rajchakit G, Chanthorn P, Kaewmesri P, Sriraman R, Lim CP (2020) Global Mittag-Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks. Mathematics 8(3):422

    Google Scholar 

  45. Rajchakit G, Chanthorn P, Niezabitowski M, Ramachandran R, Baleanu D, Pratap A (2020) Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks. Neurocomputing 417:290–301

    Google Scholar 

  46. Chanthorn P, Rajchakit G, Thipcha J, Emharuethai C, Sriraman R, Lim CP, Ramachandran R (2020) Robust stability of complex-valued stochastic neural networks with time-varying delays and parameter uncertainties. Mathematics 8(5):742

    Google Scholar 

  47. Rajchakit G, Sriraman R (2021) Robust passivity and stability analysis of uncertain complex-valued impulsive neural networks with time-varying delays. Neural Process Lett 53:581–606

    Google Scholar 

  48. Zhang Z, Zhang X, Yu T (2022) Global exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying neutral and discrete delays. Neurocomputing 490:124–131

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61873306, 62203156), the Natural Science Foundation of Heilongjiang Province (No. YQ2022F015), the China Postdoctoral Science Foundation funded project (No. 2022M720441), the Outstanding Youth Fund of Heilongjiang University (No. JCL201903), the Heilongjiang University Innovation Fund for Graduates (No. YJSCX2022-096HLJU). The authors would like to thank the associate editor and the anonymous reviewers for their helpful comments and suggestions, which greatly improves the original version of the paper.

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Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Xian Zhang, Zhongjie Zhang, Tingting Yu & Xin Wang

  2. Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, China

    Xian Zhang, Tingting Yu & Xin Wang

  3. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Tingting Yu

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  1. Xian Zhang
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Correspondence to Tingting Yu or Xin Wang.

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Zhang, X., Zhang, Z., Yu, T. et al. Global Results on Exponential Stability of Neutral Cohen–Grossberg Neural Networks Involving Multiple Neutral and Discrete Time-Varying Delays: A Method Based on System Solutions. Neural Process Lett 55, 11273–11291 (2023). https://doi.org/10.1007/s11063-023-11375-1

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